Inflate Prior or Posterior Distributions by a Variance Factor

Takes a priors or posteriors list object and inflates the variance of each distribution by a multiplicative factor while preserving the mean. This is used in staged Bayesian estimation to broaden tight posteriors from one stage before passing them as priors to the next stage, preventing weight collapse in importance sampling (particle filter / BFRS) when consecutive stages target different objectives.

The technique is known as kernel smoothing, covariance inflation, or variance tempering in the Sequential Monte Carlo literature (Liu & West 2001; Del Moral et al. 2006).

Usage

inflate_priors(
  priors,
  inflation_factor = 2,
  params = NULL,
  n_samples = 10000L,
  verbose = TRUE
)

Arguments

priors

List. A priors or posteriors object with parameters_global and parameters_location slots.

inflation_factor

Numeric scalar > 0. Variance multiplier. 2.0 doubles variance while preserving the mean. Default 2.0.

params

Optional character vector. Base parameter names to inflate. When NULL all non-fixed/frozen parameters are inflated.

n_samples

Integer. Number of samples for the empirical methods (gompertz and unrecognised distributions). Default 10000L.

verbose

Logical. Print per-parameter inflation messages. Default TRUE.

Value

A priors list with inflated distribution parameters. Metadata updated.

Methods

Each distribution is inflated using the most appropriate method:

Analytic (exact):

beta(shape1, shape2)

Reduce precision s = shape1 + shape2 by factor f. Maximum inflatable factor is f_max = s+1.

gamma(shape, rate)

shape_new = shape/f, rate_new = rate/f.

lognormal(meanlog, sdlog)

CV² scaled by f; meanlog adjusted to preserve natural-scale mean.

lognormal(mean, sd)

sd_new = sqrt(f)*sd. For either lognormal form, truncation bounds lower/upper are kept and apply to the inflated distribution.

normal(mean, sd)

sd_new = sqrt(f)*sd.

uniform(min, max)

Bounds extended symmetrically around midpoint. Skipped with a warning if new bounds violate positivity.

truncnorm(mean, sd, a, b)

sd_new = sqrt(f)*sd; the pre-truncation mean and the bounds a, b are left unchanged, so the underlying normal is inflated exactly. When a bound is active the truncated distribution's mean shifts (towards the midpoint of the bounds) and its variance grows by less than inflation_factor.

Empirical (sample → inflate → refit):

gompertz(b, eta)

No closed-form moments. Sampled empirically, variance inflated, distribution refit via MLE.

Any other distribution

Universal empirical fallback.

See also

update_priors_from_posteriors